Calculer :
( 1 / 3 ) ^ 18 * 3 ^ 20
( 2 / 3 ) ^ 11 * ( 3 / 2 ) ^ 10
( -5 / 11 ) ^ 3 * ( 11 / 5 ) ^ 4
( -3 / 4 ) ^ 6 * ( 4 / 3 ) ^ 5
Simplifier à l'aide d'un produit remarquable :
( 3 racine 2 + 5 racine 3 ) ²
[ ( racine 6 + racine 5 ) ( racine 6 - racine 5 ) ] ²
( 1 / 3 ) ^ 18 * 3 ^ 20 = 3^( -18) * 3 ^ 20 = 3²=9
( 2 / 3 ) ^ 11 * ( 3 / 2 ) ^ 10 = ( 2/3 ) ^ 11 * ( 2/3 ) ^ (-10) = (2/3)^1 = 2/3
( -5 / 11 ) ^ 3 * ( 11 / 5 ) ^ 4 = - (( 5 / 11 ) ^ 3 * ( 11 / 5 ) ^ 4)
=-(( 11 / 5 ) ^ (-3) * ( 11 / 5 ) ^ 4) = -(( 11 / 5 ) ^ 1) = - 11/5
( -3 / 4 ) ^ 6 * ( 4 / 3 ) ^ 5 = -(( 3 / 4 ) ^ 6 * ( 4 / 3 ) ^ 5)
= -(( 3 / 4 ) ^ 6 * ( 3 / 4 ) ^ (-5)) = -( 3 / 4 ) ^ 1 = -3/4
(a+b)²=a²+b²+2ab donc :
[tex](3\sqrt{2}+5\sqrt{3})^{2}= (3\sqrt{2})^{2} + (5\sqrt{3})^{2} + 2\times3\sqrt{2}\times5\sqrt{3}\\=18 + 75+30\sqrt{6} = 30\sqrt{6}+93[/tex]
(a+b)(a-b)=a²-b² donc
[tex](\sqrt{6}+\sqrt{5})(\sqrt{6}-\sqrt{5})^{2} = (6-5)^{2} =1[/tex]
Voili voilou ^^
(1/3)¹⁸*3²⁰=3⁻¹⁸*3²⁰=3²⁰⁻¹⁸=3²=9
(2/3)¹¹*(3/2)¹⁰=(2/3)¹¹*(2/3)⁻¹⁰=(2/3)¹¹⁻¹⁰=(2/3)¹=2/3
(-5/11)³*(11/5)⁴=-(11/5)⁻³*(11/5)⁴=-(11/5)⁴⁻³=-(11/5)¹=-11/5
(-3/4)⁶*(4/3)⁵=(3/4)⁶*(3/4)⁻⁵=(3/4)⁶⁻⁵=(3/4)¹=3/4
(a+b)²=a²+b²+2ab donc :
(a+b)(a-b)=a²-b² donc